This invention is in the field of communications, and is more specifically directed to multicarrier modulation communications, such as Digital Subscriber Line (DSL) communications.
An important and now popular modulation standard for DSL communication is Discrete Multitone (DMT). According to DMT technology, the available spectrum is subdivided into many subchannels (e.g., 256 subchannels of 4.3125 kHz). Each subchannel is centered about a carrier frequency that is phase and amplitude modulated, typically by Quadrature Amplitude Modulation (QAM), in which each symbol value is represented by a point in the complex plane. The number of available symbol values for each subchannel, and thus the number of bits in each symbol communicated over that subchannel, is determined during initialization of the DMT communications session. The number of bits per symbol for each subchannel (i.e., the “bit loading”) is determined according to the signal-to-noise ratio (SNR) at the subchannel frequency, which is affected by the transmission channel noise and the signal attenuation at that frequency. For example, relatively noise-free and low attenuation subchannels may communicate data in ten-bit to fifteen-bit symbols, represented by a relatively dense QAM constellation with short distances between points in the constellation. On the other hand, noisy channels may be limited to only two or three bits per symbol, allowing a greater distance between adjacent points in the QAM constellation. Indeed, the SNR of some subchannels is so poor that these subchannels are unloaded, carrying no bits. DMT modulation thus maximizes the data rate over each subchannel, permitting high speed access to be carried out even over relatively noisy and attenuated twisted-pair lines.
DMT modulation also permits much of the signal processing to be carried out in the digital domain. Typically, a serial digital datastream to be transmitted is arranged into symbols, one for each subchannel, with the symbol size depending on the bit loading, as noted above. Reed-Solomon coding and other coding techniques are typically applied for error detection and correction. Modulation of the subchannel carriers is obtained by application of an inverse Discrete Fourier Transform (IDFT) to the encoded symbols, producing a discrete modulated time domain signal having signal components at each of the subcarrier frequencies. This modulated signal is then serially transmitted. All of these DMT modulation operations can be carried out in the digital domain, permitting implementation of much of a DSL modem, and particularly much of the processing-intensive operations, in a single chip such as a Digital Signal Processor (DSP).
The discrete output time domain signal from the modulation is converted into a time-domain analog signal by a conventional digital-to-analog converter, and is communicated over the transmission channel to the receiving modem, which reverses the process to recover the transmitted data. Ideally, the DMT subchannels in the received signal are orthogonal so that the signal can be demodulated by a Discrete Fourier Transform (DFT).
However, the non-ideal impulse response of the transmission channel distorts the transmitted signal. The signal received by the receiving modem can be considered to be a convolution of the transmitted analog signal with the impulse response of the transmission channel. One may express the time-domain signal y(n) at the receiver, based on a transmitted time-domain signal x(n), as:y(n)=x(n){circle around (×)}h(n)This expression simply states that the received signal y(n) is the time-domain convolution of the input signal x(n) with the channel impulse response h(n). In the ideal case, this time-domain expression can be expressed in the frequency-domain as:Y(n)=X(n)·H(n)where X(n), H(n), and Y(n) are the respective frequency-domain representations of time-domain signals x(n), h(n), y(n). Considering that the transmitted signal x(n) is the IDFT of the symbol sequences at their respective subchannel frequencies, the frequency-domain spectrum X(n) corresponds to the symbols themselves. According to the DMT modulation technology, the receiver can therefore retrieve the symbols X(n) by removing the channel response H(n) from the DFT of the frequency-domain received signal Y(n). Conventionally, this is performed by a single-tap frequency domain equalizer.
However, time domain convolution corresponds to frequency domain multiplication only if the input sequence is infinitely long, or if the input sequence is periodic. Because the number of subchannels is finite, however, the number of real-valued time-domain samples at the output of the transmitter IDFT (i.e., the “block” length) is also finite. Accordingly, it is useful to make the transmitted signal appear to be periodic, at a period on the order of the block length. A well-known technique for accomplishing this is to include a cyclic prefix with each transmitted block in the datastream. The cyclic prefix is generally defined as a number P of samples at the end of a block of samples in the output bitstream. These P samples are prepended to the block, prior to digital-to-analog conversion, so that the transmitted signal appears periodic. This apparent periodicity in the input sequence permits the use of a DFT to recover the modulating symbols in each subchannel, so long as the impulse response of the transmission channel, commonly referred to as the channel length, is less than the length of the cyclic prefix.
In effect, the cyclic prefix eliminates inter-symbol interference (ISI) between adjacent data frames, and inter-carrier interference (ICI) among subchannels. ISI generally arises from distortion and spreading of the transmitted signal over the channel, causing the end of one DMT symbol to overlap into the beginning of the next DMT symbol. ICI affects the independence of the subcarriers, resulting in loss of orthogonality among the subchannels, which in turn prevents separation of the modulating data on these subchannels at the receiver.
In order for the input sequence to appear periodic, so that ISI is contained within the redundant prefix of the block, the cyclic prefix must be longer than the channel length. However, this causes the effective data rate of the transmission to be reduced accordingly. In the case of a signal with a block length of N samples and a cyclic prefix of P samples generated by prepending a copy of the last P samples of the block, the data rate is reduced by the factor:
  N      N    +    P  This presents a tradeoff between interference and data rate in conventional DMT communications.
FIG. 1 functionally illustrates an example of a conventional DSL communication system. In the system of FIG. 1, only one direction of transmission (from transmitting modem 10 over transmission channel H to receiving modem 20) is illustrated. It will of course be understood by those skilled in the art that data will also be communicated in the opposite direction, in which case modem 20 will be the transmitting modem and modem 10 the receiving modem.
Transmitting modem 10 receives an input bitstream that is to be transmitted to receiving modem 20. This input bitstream may be generated by a computer at the same location (e.g., the central office) as transmitting modem 10, or alternatively and more likely is generated by a computer network, in the Internet sense, that is coupled to transmitting modem 10. The input bitstream is a serial stream of binary digits, in the appropriate format as produced by the data source.
Bit-to-symbol encoder function 11 in transmitting modem 10 groups the bits of the input bitstream into multiple-bit symbols, according to the bit loading assigned to each subchannel in the initialization of the communication session. These symbols will modulate the various subchannels of the DMT signal. Optionally, error correction coding, such as Reed-Solomon coding for error detection and correction purposes, or trellis coding, may also be applied at encoder 11 for additional signal-to-noise ratio improvement.
The symbols generated by encoder function 11 are typically complex symbols, including both amplitude and phase information, and correspond to points in the appropriate modulation constellation (e.g., quadrature amplitude modulation, or QAM) for each subchannel, as determined upon initialization. The encoded symbols for each block are then applied to inverse Discrete Fourier Transform (IDFT) function 12. IDFT function 12 associates each input symbol with one subchannel in the transmission frequency band, and generates a corresponding number of time domain symbol samples according to the Fourier transform. These time domain symbol samples are then converted into a serial stream of samples by parallel-to-serial converter 13. Typically, if N/2 complex symbols are presented to IFFT function 12, IFFT function 12 outputs a block of N real-valued time domain samples. Those skilled in the art having reference to this specification will readily recognize that each of functions 11 through 13 may be carried out, and preferably actually are carried out, as digital operations executed by a digital signal processor (DSP).
In function 14, the cyclic prefix (CP) is then added into the signal, typically by prepending the last ν samples of each frame to the beginning of that frame, as discussed above. Digital filtering function 15 then processes the datastream, by interpolating to increase the sample rate, digital low pass filtering to remove image components, and digital high pass filtering to eliminate POTS-band interference. The digitally-filtered datastream signal is converted to analog by digital-to-analog converter 16, and low-pass filtered by analog filtering function 18, prior to transmission. As described in U.S. Pat. No. 6,226,322, commonly assigned herewith and incorporated herein by this reference, digital filter function 15, digital-to-analog converter 16, and analog filter function 18 are preferably implemented in a conventional codec circuit, such as a member of the TLV320AD1x device family available from Texas Instruments Incorporated.
The output of analog filter 18 is then forwarded to transmission channel H and in turn to receiving modem 20 by conventional line driver and receiver circuitry, such as the THS7102 line driver/receiver available from Texas Instruments Incorporated, and by a conventional hybrid circuit. In the case of ADSL communications, transmission channel H is physically realized by twisted-pair wire. The significant distortion and noise added to the transmitted analog signal by transmission channel H is represented by its impulse response h(n), as described above.
The downstream transmitted signal is received by receiving modem 20, which, in general, reverses the processes of transmitting modem 10 to recover the information of the input bitstream. As shown in FIG. 1, analog filter function 21 processes the received signal prior to analog-to-digital conversion function 22, which converts the filtered analog signal to digital. Conventional digital filtering function 23 is then applied to augment the function of the analog filters. The combination of analog and digital filter functions 21, 23 also preferably includes some frequency band filtering to isolate the received signal from signals currently being transmitted upstream by modem 20.
In this conventional arrangement, time domain equalizer (TEQ) 24 is preferably a finite impulse response (FIR) digital filter, designed to effectively shorten the length of the impulse response of the transmission channel H, taking into account the filtering performed by functions 21, 23. The design of this digital filter is realized by the selection of the particular coefficients of the FIR implementing TEQ function 24 during initialization, or “training”, of the combination of modems 10 and 20 as the communications session is established. The cyclic prefix is then removed by function 25. Serial-to-parallel converter 26 converts the filtered datastream into a number of samples for application to Discrete Fourier Transform (DFT) function 27. Because the received signal is a time-domain superposition of the modulated subchannels, DFT function 27 will recover the modulating symbols at each of the subchannel frequencies, reversing the IDFT performed by function 12 in transmitting modem 10 to produce a frequency domain representation of a block of transmitted symbols, multiplied by the frequency-domain response of the effective transmission channel. The cyclic prefix of the data frame is at least as long as the channel response h(t), shortened by TEQ function 24. Based on this assumption, frequency-domain equalization (FEQ) function 28 divides out the frequency-domain response of the effective channel, and recovers an estimate of the modulating symbols. Symbol-to-bit decoder function 29 then resequences the recovered symbols, decodes any encoding that was applied in the transmission of the signal, and produces an output bitstream that is an estimate of the input bitstream upon which the transmission was based. This output bitstream is then forwarded to a client workstation or other recipient.
As noted above, time domain equalizer (TEQ) function 24 shortens the effective channel length of the transmission channel, to ensure that the length of the cyclic prefix is at least as long as the channel response, so that the transmitted signal can be successfully recovered by FEQ function 28 without significant ISI and ICI. In conventional modem training sequences, performed upon initiation of a DSL communications session, the TEQ coefficients are optimized to reduce the channel response as much as possible. While the channel response is necessarily frequency dependent, conventional TEQ optimization is performed simultaneously over all channels. As a result, conventional TEQ optimization is not suited for optimizing the signal-to-noise performance of the subchannels. As such, conventional TEQ training does not result in optimum bitloading capacity for the DSL communications session.
It is known to define the equalization for DMT receiver systems on a per-tone basis, as described in Van Acker et al., “Per-tone Equalization for DMT-Based Systems”, IEEE Trans. on Comm., Vol. 49, No. 1 (IEEE, January 2001), pp. 109–119. This per-tone equalization improves the overall performance of the system, because the equalizer is defined based on the channel response for each subchannel individually. Theoretically, the per-tone equalization design can optimize the capacity of each subchannel, while still also ensuring that the channel response is minimized.
By way of further background, the theory behind the per-tone equalization described by Van Acker et al. will now be summarized. If one considers vector y to be a perfectly aligned DMT frame of N samples, with a cyclic prefix of length ν samples:y=[y0, y1, . . . , yN+ν−2,yN+ν−1]Referring back to FIG. 1, the receipt of the frame y by receiving modem 20 is accomplished by applying TEQ function 24 to frame y. DFT function 27 demodulates this signal, and FEQ function 28 recovers an estimate Z of the originally transmitted signal. This process can be expressed by:
      [                                        Z            1                                                ⋮                                                  Z            N                                ]    =            [                                                  D              1                                            0                                ⋯                                                0                                ⋰                                0                                                ⋮                                0                                              D              N                                          ]        ·          F      N        ·          (              Y        ·                  w          teq                    )      where wteq=[w0, w1, . . . , wν−1]T and is the real-valued ν-tap TEQ function 24. In this representation, matrix Y is the set of frames of time domain samples for the inputs of ν FFTs associated with a time t, ν being the length of the cyclic prefix and at least as large as the combined impulse response of the transmission channel and TEQ function 24:
  Y  =            [                        y                      t            ,            0                          ⁢                                  ⁢                  y                      t            ,            1                          ⁢                                  ⁢        …        ⁢                                  ⁢                  y                      t            ,                          v              -              1                                          ]        =          [                                                  y              v                                                          y                              v                -                1                                                          ⃛                                              y              1                                                                          y              v                                            ⋰                                ⋰                                              y              2                                                            ⋮                                ⋰                                ⋰                                ⋮                                                              y                              N                +                v                -                1                                                                        y                              N                +                v                -                2                                                          ⋯                                              y              N                                          ]      The matrix FN is the N×N FFT matrix of DFT function 27, and the coefficients Di constitute the complex 1-tap FEQ function 28. This expression applies a single FFT operation FN·(Y·wteq), as known in the art. Van Ackel et al. state that one can reorder this representation of the receiver demodulation, combining the TEQ and FEQ operations:Zi=Di·rowi(FN)·(Y·wteq)=rowi(FN·Y)·wteq·Di for each tone Zi. In effect, by moving the FEQ Di to the right of this expression, a combined complex ν-tap FEQ for the ith tone is derived as:wteq·Di=(wfeq,i)ν×1 However, this approach requires the ν FFTs represented by FN·Y. According to this approach, each tone i has its own, optimized, TEQ function that is implemented in the form of a ν-tap FEQ. This optimized TEQ can be determined by considering the ν FFTs of FN·Y as:
                              Y          FFT                =                              ⌊                                          y                                  fft                  ,                  0                                            ⁢                                                          ⁢                              y                                  fft                  ,                  1                                            ⁢                                                          ⁢              …              ⁢                                                          ⁢                              y                                  fft                  ,                                      v                    -                    1                                                                        ⌋                    =                                    F              N                        ⁢            Y                                                            and:                ⁢                                  ⁢                              W            f                    =                                    [                                                                                          w                                              feq                        ,                        0                                            T                                                                                                                                  w                                              feq                        ,                        1                                            T                                                                                                            ⋮                                                                                                              w                                              feq                        ,                                                  N                          -                          1                                                                    T                                                                                  ]                        =                          [                                                w                                      f                    ,                    0                                                  ⁢                                                                  ⁢                                  w                                                            f                      ,                      1                                        ⁢                                                                                                                ⁢                …                ⁢                                                                  ⁢                                  w                                      f                    ,                                          v                      -                      1                                                                                  ]                                          In this approach, yfft,i is an N×1 vector corresponding to the FFT of the ith column of matrix Y. The equalizer coefficient vector wf,i is an N×1 vector of the ith equalizer coefficients for all tones.
As noted above, this approach, as described in Van Acker et al., requires v FFTs per symbol, rather than only a single FFT operation as in the conventional approach of FIG. 1. Van Acker et al. describe, however, that the Toeplitz structure of matrix Y permits the ν FFTs to be calculated efficiently as a sliding FFT, requiring the calculation of only one full FFT, with the other ν−1 FFTs calculated by:
      y          fft      ,      m        =                    y                  fft          ,                      m            -            1                              ⊗      p        +                            [                                                    1                                                                    ⋮                                                                    1                                              ]                          N          ⨯          1                    ·              (                                            y                              t                ,                m                                      ⁡                          (              0              )                                -                                    y                              t                ,                                  m                  -                  1                                                      ⁡                          (                              N                -                1                            )                                      )            where {circle around (×)} is a component-wise multiplication and where matrix p is:
      p    =                  [                              α            0                    ⁢                                          ⁢                      α            1                    ⁢                                          ⁢          …          ⁢                                          ⁢                      α                          N              -              1                                      ]            T        ,            for      ⁢                          ⁢      α        =          ⅇ              -                  j2π          ⁡                      (                          1              N                        )                              and for m=1, . . . , ν−1. The difference of yt,m(0)−yt,m−1(N−1) is the difference between the first and last elements of yt,m and yt,m−1, respectively. As a result, for each tone i, all relevant FFT elements can be derived as linear combinations of the ith component of the FFT of the first column of matrix Y and the ν−1 difference terms yt,m(0)−yt,m−1(N−1) for m=1, . . . ,ν−1.
This per-tone approach is intended to optimize the signal-to-noise ratio, and thus the bit-loading, of each tone in the DMT signal. With each tone optimized for SNR, this approach theoretically optimizes the equalization and capacity performance of the entire DMT modem communications session. Simulations have been performed, in connection with this invention, that indicate that this theoretical potential can be realized.
However, it has also been observed, in connection with this invention, that the per-tone equalization approach described by Van Acker et al. is subject to several significant limitations when realizing this approach in actual DMT modems for DSL communications. A large amount of memory is required to store all of the intermediate FFT results and also the per-tone equalizer coefficients, and a high memory access bandwidth is necessary to access all of these values at a reasonable clock rate. The computational complexity for computing the ν−1 sliding FFTs, especially during a DSL session in which the equalizer taps ought to be updated to account for channel variation, is also a limitation on this approach.
While the memory capacity, memory access bandwidth, and computational power constraints may become less of an issue as time passes, an insurmountable constraint is presented by the current ITU communications standards, including the G.dmt and G.dmt.bis standards (ITU-T, G.992.1 : Asymmetrical Digital Subscriber Line (ADSL) Transceivers; ITU-T, Draft G.dmt.bis: Asymmetrical Digital Subscriber Line (ADSL) Transceivers). According to these and previous standards, the TEQ coefficients are established early in the DSL training sequence, typically in the “Reverb” sequence that immediately follows the pilot tone, as the TEQ coefficients must be established before the “Message Exchange” sequence can be successfully performed. However, the derivation of the per-tone equalizer coefficients according to the Van Acker approach described above requires a pseudo-random sequence, which is not initiated under current standards until the “Medley” sequence, which is after the “Reverb” and “Message Exchange” sequences. As a result, per-tone equalization according to known technology is not available for DSL receiver modem architectures under current standards.